Question

The table of values represents a polynomial function f(x)
How much greater is the average rate of change over the interval [7,9] than the interval [4,6]

Answer 1

Answer:

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Answer 2

x            f(x)

4           358

5           690

6           1178

7           1852

8           2742

9           3878

Average rate of change over [ 7, 9 ] = [ f(9) - f(7) ] / (7 - 5)

= [ 3878 - 1852 ] / (7 - 5)

= 2026 / 2

∴ Average rate of change over [ 7, 9 ] = 1013

Average rate of change over [ 4, 6 ] = [ f(6) - f(4) ] / (6 - 4)

= [ 1178 - 358 ] / (6 - 4)

= 820 / 2

∴ Average rate of change over [ 4, 6 ] = 410

1013 - 410 = 603

1013 is 603 times greater than 410.